ECE 3410 Homework 4 (C) (B) (A) (F) (E) (D) (H) (I) Solution. Utah State University 1 D1 D2. D1 v OUT. v IN D1 D2 D1 (G)
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1 ECE 341 Homework 4 Problem 1. In each of the ideal-diode circuits shown below, is a 1 khz sinusoid with zero-to-peak amplitude 1 V. For each circuit, sketch the output waveform and state the values of the maximum and minimum output voltages. For this problem, use the ideal switch model of the diode. (A) (B) (C) D3 (D) (E) (F) (G) (H) (I) Utah State University 1
2 ECE 341 Homework 4 (cont.) (A) 1 (B).5 (C) (D) 1 (E) (F) (G).5 (H) 2 4 (I) Utah State University 2
3 ECE 341 Homework 4 Problem 2. The circuit shown below uses a diode in the feedback path of the op amp. For each question, use only the ideal switch model to analyze the circuit s behavior (i.e. ignore the diode s.7v forward drop). Assume that 1 = 1kΩ, 2 = 4kΩ, and the op amp is ideal. 2 1 i 1 (A) Suppose = 2V. What direction is the current i 1 passing through 1? Is the diode ON or OFF? What is? The current is passing forward (left to right), so the diode should be ON and we expect = V since it is shorted to the virtual ground at the op amp s inverting input terminal. (B) Suppose = 2V. What direction is the current i 1 passing through 1? Is the diode ON or OFF? What is? In this case the current is passing backward (right to left), so the diode is reverse biased and should be OFF. With the diode deactivated, the circuit should behave like an ordinary inverting configuration with = 2 1 = 8 V. Problem 3. The circuit shown below uses a diode in the feedback path of the op amp. For each question, use only the ideal switch model to analyze the circuit s behavior (i.e. ignore the diode s.7v forward drop). Assume that = 1kΩ, and the op amp is ideal. Utah State University 3
4 ECE 341 Homework 4 D i i (A) Suppose = 2V. What direction is the current i passing through? Is the diode ON or OFF? What is? With positive, if the diode is OFF then the op amp will rail in the positive direction, so the diode will turn ON. Then the current i flows in the forward direction (consistent with the diode being ON). Since the feedback loop is closed, the op amp will regulate = = 2 V. (B) Suppose = 2V. What direction is the current i passing through 1? Is the diode ON or OFF? What is? With negative, if the diode is OFF then the op amp will rail in the negative direction, so the diode will stay OFF. In that case there is no current passing through and = V. (C) Explain why can never be less than V. If is ever negative, then current will have to flow backwards through, and then backwards through the diode. Since the diode will block any reverse current, this case is impossible. Utah State University 4
5 ECE 341 Homework 4 Problem 4. A half-wave rectifier circuit is shown below. You may assume that = 1kΩ and the diode D has a.7v forward drop when its forward current equals 1mA. i (A) Using the iterative analysis procedure, solve a precise solution for i and for the case when = 2V. Show your results at each iteration, and state the number of iterations required to reach three significant digits of precision. We start with the initial guess that v D =.7 V and i D = 1 ma. We then iterate these steps: i. Solve = v D and update i D = /. ii. Solve v D =.7 V 26 mv ln (i D /1 ma). Then the table of iterations is as follows: v D i D v D i D After three iterations (four rows including the initial guess) we can verify there is no change in the three most significant digits. (B) Using the small-signal model, solve an approximate solution for i and for the case when = 2V. How close is the small-signal result compared to the iterative method, and compared to the constant voltage drop method? Using the linearized method, we insert a 26 Ω resistor to account for the error in our initial guess. Then we have this equivalent circuit: Utah State University 5
6 ECE 341 Homework 4 (cont.) 26 Ω.7 V 1 ma NOT FINISHED YET!!! (C) epeat the iterative and small-signal solutions for the case when =.5V. How do they compare in this case? Problem 5. A.7V regulator circuit is shown below. You may assume that = 1kΩ and the diode has a.7v forward drop at 1mA. v in v out i (A) Suppose has a sinusoidal ripple such that its maximum and minimum values are (max) = 3.5V (min) = 3.V Using the small-signal procedure, estimate the maximum and minimum values that will appear at. Calculate your answer with mv precision. (B) Calculate the line regulation, defined as the ratio Give your result in mv/ V. L = (max) (min) (max) (min) Problem 6. The peak rectifier circuit shown below is used to convert a 1kHz AC signal into a DC signal. The input signal has a zero-to-peak amplitude of 15V. The input signal also Utah State University 6
7 ECE 341 Homework 4 has a frequency f = 1kHz and period T = 1ms. The resistor and capacitor values are C = 1µF and = 1kΩ, respectively. The diode has a.7v forward drop when its forward current is 1mA. C (A) Assuming that charges all the way up to 15V during the positive cycle of, calculate the ripple amplitude V r that happens during the period when the diode is OFF. Note that, since C T, if the diode switches OFF at some time t then we may approximate as 15V t t C (B) Calculate the ripple amplitude when f is increased to 1kHz. Problem 7. The half-wave precision rectifier circuit suffers from three problems: First, when the diode is off, the feedback loop becomes an open-circuit and the op amp is driven to a rail voltage. Second, when the diode turns on again, the op amp must slew back from the rail, which delays its response. Third, only half of the waveform is rectified. The circuit shown below rectifies (ehem) these problems. Study the circuit and answer the following questions. vx v Y L D3 D4 Utah State University 7
8 ECE 341 Homework 4 (A) First, let = V and suppose has a (very large) open-loop gain A but is otherwise ideal. Using the ideal switch model, predict the voltages that will appear at v X, v Y and. (B) Now let = 1 mv. Using the ideal switch model for the diodes, predict which diodes will be on and which will be off, and report the state (ON/OFF) for each diode. Is the op amp s negative feedback loop closed? Predict the value at v Y, v X and. (C) Now let = 1 mv. Again using the ideal switch model, predict which diodes will be on and which will be off, and report the state for each diode. Is the op amp s negative feedback loop closed? Predict the value at v Y, v X and. (D) If you use the diode s full exponential model instead of the ideal switch model, how will your results change for the last two sub-problems? You may state your answer symbolically, in terms of the diodes unknown forward voltage drop, v D. Utah State University 8
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